Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu¹ ; Cai-Feng Yi²

¹ Department of Informatics and Engineering Jingdezhen Ceramic Institute (XiangHu XiaoQu) Jingdezhen, Jiangxi 333403, China
² Institute of Mathematics and Informatics Jiangxi Normal University Nanchang, Jiangxi 330027, China

Annales Polonici Mathematici, Tome 97 (2010) no. 2, pp. 123-136.

Résumé

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $$ f^{(k)}+a_{k-1}(z)f^{(k-1)}+\cdots+a_1(z)f' +D(z)f=0, \tag{1}$$ where $D(z)=Q_1(z)e^{P_1(z)}+Q_2(z)e^{P_2(z)}+Q_3(z)e^{P_3(z)}$, $P_1(z), P_2(z), P_3(z)$ are polynomials of degree $n\geq1$, $Q_1(z),Q_2(z),Q_3(z),a_j(z)$ $(j=1,\ldots,$ $k-1)$ are entire functions of order less than $n$, and $k\geq2$.

Détail

DOI : 10.4064/ap97-2-2

Keywords: investigate exponent convergence zero sequence solutions differential equation k k cdots tag where polynomials degree geq ldots k entire functions order geq